A committee markup of a bipartisan health bill from Sens. Lamar Alexander and Patty Murray could add another potentially fatal complication for the measure that is already under significant pressure.

Senators from both parties have for months decried the lack of regular order in the chamber as Republicans tried to jam through legislation to repeal the 2010 health law.

Now, after the proposal from the duo that helms the Senate Health, Education, Labor and Pensions Committee solicited enough support on Thursday to pass the chamber if a vote were held, sponsors are unclear on how the bill will advance.

“We haven’t made a decision on that yet,” Alexander, a Republican from Tennessee, said when asked whether a markup will be held.

Both Republican leaders and Democrats on HELP, however, said the committee process would be necessary.

“I think our folks will want to have regular order on that,” Senate Republican Conference Chairman John Thune of South Dakota said.

When the 2010 health law was advancing through the Senate, the health panel held a 13-day markup of the legislation. The Senate Finance Committee held an eight-day markup.

While the legislation from Alexander and Murray is much smaller and focuses on providing short-term relief to the insurance markets, a markup of the bill could devolve into a bitter and partisan battle over the law.